Question

When making a batch of orange juice for her basketball team, Jackie used 5 times as much water as concentrate. There were 32 more cups of water than concentrate.
a. How much juice did she make in all?
b. She poured the juice into quart containers. How many containers could she fill?

Answer 1

Answer:

(a) 48 cups juice.

(b) 12 quart containers.

Step-by-step explanation:

Let x represent number of cups of concentrate used by Jackie.

(a) We have been given that while making a batch of orange juice for her basketball team, Jackie used 5 times as much water as concentrate.

The amount of water would be $5x$.

We are also told that there were 32 more cups of water than concentrate. We can represent this information in an equation as:

$5x=x+32$

Let us solve for x.

$5x-x=x-x+32$

$4x=32$

$\frac{4x}{4}=\frac{32}{4}$

$x=8$

The total amount of juice would be amount of concentrate plus water: $x+5x\Rightarrow 6x =6\times 8 =48$

Therefore, Jackie used 48 cups of juice.

(b). To find the amount of quart containers that can be filled by 48 cups of juice, we will convert 48 cups to quarts.

1 cup = 0.25 quart.

$\text{Number of quart containers}=48\times 0.25$

$\text{Number of quart containers}=12$

Therefore, Jackie can fill 12 quart containers.